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  Volume 6, Number 2, April 2021 , pages 153-168

Viscoelastic inhomogeneous beam under time-dependent strains: A longitudinal crack analysis
Victor I. Rizov

    The present paper is concerned with analysis of two longitudinal cracks in a viscoelastic inhomogeneous cantilever beam. The loading of the beam is applied by two stages. At the first stage, the strains increase with time at a constant speed up to a given magnitude. At the second stage, the strains remain constant with time. The viscoelastic behavior of the beam is described by using a viscoelastic model with a linear spring in series with a linear dashpot and a second linear dashpot connected parallel to the spring and the first dashpot. Stress-strain-time relationships of the viscoelastic model are derived for both stages (at increasing strain and at constant strain with time). Time-dependent strain energy release rates are obtained for both longitudinal cracks by analyzing the balance of the energy. Solutions to the time-dependent strain energy release rate are derived also by considering the time-dependent strain energy stored in the beam structure. The solutions are used to analyze the change of the strain energy release rate with time at both stages of loading.
Key Words
    longitudinal crack; viscoelastic beam; inhomogeneous material; time-dependent strain; analytical study
Victor I. Rizov: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria

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